In an A.P. the pth term is q and the (p + q)th term is 0. Then the qth

1.	In an A.P. the pth term is q and the (p + q)th term is 0. Then the qth term is(A) – p(B) p (C) p + q (D) p – q
Answer» (B) is the correct answer Let a, d be the first term and common difference respectively Therefore, T_p = a + (p – 1) d = q and ... (1) T_{p+ q} = a + (p + q – 1) d = 0 ... (2) Subtracting (1), from (2) we get qd = – q Substituting in (1) we get a = q – (p – 1) (–1) = q + p – 1 Now T_q = a + (q – 1) d = q + p – 1 + (q – 1) (–1) = q + p – 1 – q + 1 = p

In an A.P. the pth term is q and the (p + q)th term is 0. Then the qth term is(A) – p(B) p (C) p + q (D) p – q

Answer»

(B) is the correct answer

Let a, d be the first term and common difference respectively

Therefore,

T_p = a + (p – 1) d = q and ... (1)

T_{p+ q} = a + (p + q – 1) d = 0 ... (2)

Subtracting (1), from (2) we get

qd = – q

Substituting in (1) we get

a = q – (p – 1) (–1) = q + p – 1

Now

T_q = a + (q – 1) d = q + p – 1 + (q – 1) (–1)

= q + p – 1 – q + 1 = p